A guinea worm is extracted by a health worker from a child's foot in Savelugu, Ghana. Photograph: Olivier Asselin/AP

The world is tantalisingly close to eradicating guinea worm disease, which would make it only the second disease of humans to be wiped from the planet, according to former US president Jimmy Carter.

Speaking in London alongside World Health Organisation director general Dr Margaret Chan, Carter, who has led the fight against the disease, said that around £60m more was needed to finish the job.

Since the Carter Centre took up the cause in 1986, almost every nation had eradicated the crippling and painful disease, said the former president. "It is likely by the end of this year we will have guinea worm in only one country – the newest one on earth – South Sudan," he added.

In 1995 Carter personally negotiated a six-month ceasefire between northern and southern Sudan, in a successful attempt to reach remote villages where guinea worm larvae infest drinking water, causing immense suffering to some of the poorest men, women and children on earth.

"The Carter Centre's programme is designed to go into the places where the needs are greatest and quite often where the needs are neglected by others," said the former president. "We couldn't get into southern Sudan because of the war."

In 1995 the leaders of north and south agreed the longest-ever ceasefire in the conflict, enabling volunteers to reach remote rural villages. They knew, said Carter, that "guinea worm was a blight on the people. There was an inseparable connection between peace on the one hand and doing away with guinea worm on the other." Carter eventually helped negotiate peace and his centre monitored the national elections in 2010 and the referendum on separation this year.

Since 1986, 3.5m cases of guinea worm disease in 21 countries have been reduced by 99.9%. Now there are fewer than 1,000 a year.

In 1979, while Carter was president, the eradication of smallpox was declared. That cost £195m and was achieved through mass vaccination – a feat that is being attempted in polio but which looks difficult to repeat with the increased movement of populations.

Guinea worm eradication, a generation later, has so far cost £250m and is close to being achieved without recourse to vaccination or treatments, because they do not exist. The disease is being prevented through the drilling of wells for uncontaminated water and education of those who live in remote rural villages. People have been taught to filter their drinking water through a small pipe, cheaply made and distributed, which removes the guinea worm larvae.

The effort to reach the remotest villages has paid dividends, said Carter. "When we go in to a place like South Sudan, we have personally trained about 12,000 local volunteers and taught them aspects of healthcare and about good water that is clean to drink. We have often been able to dig deep wells that are free from disease."

There have been other benefits too. "In the rest of their lives, many have never known success. They have never attempted anything that really succeeded. Quite often their relationship to foreigners has comprised broken promises. When we go in and teach them how they can correct their own problem, they not only learn the rudiments of healthcare and sanitation but they learn how to be self-sufficient and gain self-respect," he said.

Stephen O'Brien, international development minister, pledged on Wednesday the UK government would provide up to one-third of the funding needed for the campaign against the guinea worm. But the amount of the British donation is dependent on how much is put in by others – the Department for International Development will put in £1 for every £2 from elsewhere, he said.

O'Brien added that discussions were taking place with other donors, but that it would be premature to reveal their identities. "I very much hope they will produce a response to the challenge," he said.